Question: Solve for $x$ and $y$ using elimination. ${5x-4y = -1}$ ${4x+y = 16}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${5x-4y = -1}$ $16x+4y = 64$ Add the top and bottom equations together. $21x = 63$ $\dfrac{21x}{{21}} = \dfrac{63}{{21}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {5x-4y = -1}\thinspace$ to find $y$ ${5}{(3)}{ - 4y = -1}$ $15-4y = -1$ $15{-15} - 4y = -1{-15}$ $-4y = -16$ $\dfrac{-4y}{{-4}} = \dfrac{-16}{{-4}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {4x+y = 16}\thinspace$ and get the same answer for $y$ : ${4}{(3)}{ + y = 16}$ ${y = 4}$